- #1

rock.freak667

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## Homework Statement

[tex]f:\rightarrow x+1,g:x\rightarrow |x|[/tex]

Solve the equation gf(x)=fg(x)

## Homework Equations

## The Attempt at a Solution

gf(x)=|x+1|

and fg(x)=|x|+1

so I drew the graphs of y=gf(x) and y=fg(x) on the same axes.

For x<0 the graphs do not intersect as the two lines are parallel (having the same gradient) and hence there is no solution for x<0.

BUT, for x>0, the two lines are the same...so that means there are an infinite number of solutions for x>0. Does that mean I write the answer as {x:x>0} ?